Mathematics I207710 marksNumerical: Improper integrals and limitsImproper integrals
Show that the following integrals converge and diverge respectively. If f(x,y) = fracxyx2 + y2, does lim(x,y) to (0,0) f(x,y) exist? A particle moves in a straight line and has acceleration given by a(t) = 6t2 + t. Its initial velocity is 4 m/sec and its initial displacement is s(0) = 5 cm. Find its
Show that the following integrals converge and diverge respectively.
$$\int_1^{\infty} \frac{1}{x^2} dx \text{ and } \int_1^{\infty} \frac{1}{x} dx$$
If $f(x,y) = \frac{xy}{x^2 + y^2}$, does $\lim_{(x,y) \to (0,0)} f(x,y)$ exist?
A particle moves in a straight line and has acceleration given by $a(t) = 6t^2 + t$. Its initial velocity is $4$ m/sec and its initial displacement is $s(0) = 5$ cm. Find its position function $s(t)$.
[2+3+5]
- Integrals: $\int1^{\infty} \frac{1}{x^2},dx$ and $\int1^{\infty} \frac{1}{x},dx$ - Function: $f(x,y) = \dfrac{xy}{x^2+y^2}$; limit as $(x,y)\to(0,0)$ - Acceleration: $a(t) = 6t^2 + t$ - Initial velocity: $v(0) = 4$ m/s - Initial displacement: $s(0) = 5$ cm Note on units: $v(0)$ is given in m/...